Cyclic $m$-Cycle Systems of $K_{n,n}$ for $m\leq100$

Yuge Zheng 1，2
1 Department of Mathematics, Shanghai Jiao Tong University,
Shanghai 200240, P. R. China
2 Henan Polytechnic University, Jiaozuo 454000, P. R. China

Abstract     Full Text  PPT


Let $K_{n,n}$ denote the complete bipartite graph with $n$ vertices in each part. In this paper, we will determine necessary and sufficient conditions for the existence of cyclic m-cycle systems of $K_{n,n}$ for integers $30<m\leq100$. As a consequence, necessary and sufficient conditions are determined for the existence of cyclic m-cycle systems of $K_{n,n}$ for all integers $m\leq100$.